Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity, non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics—a state of affairs not envisioned by Husserl, for whom science recast natural ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered